This book is dedicated to the general study of the structural dynamics of direct and inverse problems. The models used in the industry to perform dynamic calculations are intended to learn about the frequencies and modes of the studied structure in its solicitation usual range. The associated calculations are large. From this follows a simple idea: reduce the size of the matrices associated with a system that least affected the simulation results, both quantitatively and qualitatively. The challenge is bold in some cases. Different ways of doing reduce the order of the matrices into play to make the calculation on a smaller problem and transcribe the results to the size of the original problem. We also present the structural identification techniques: technical coupling between calculated and measured data to develop a reliable mathematical model. It seeks to build a mathematical model for the purpose of assisted conception and predicting the behavior and responses in the presence of a given excitation field (sizing problems, rupture, fatigue ...). It also seeks the prediction of performance and safety limits. This identification occurs to evaluate some dynamic characteristics currently not accessible by calculating correct some approximations or uncertainties.